% Mizar problem: t17_aofa_i00,aofa_i00,1516,5 
fof(t17_aofa_i00, conjecture,  (! [A] :  (m4_aofa_i00(A) =>  (! [B] :  ( (v1_funct_1(B) &  (v1_funct_2(B, k9_funct_2(k4_ordinal1, k4_numbers), k4_ordinal1) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k9_funct_2(k4_ordinal1, k4_numbers), k4_ordinal1)))) )  => m2_aofa_i00(B, k7_freealg(k19_aofa_000, k26_aofa_i00), k4_ordinal1, k1_aofa_i00(k9_funct_2(k4_ordinal1, k4_numbers), k5_numbers, k5_numbers), A)) ) ) ) ).
fof(abstractness_v1_lang1, axiom,  (! [A] :  (l1_lang1(A) =>  (v1_lang1(A) => A=g1_lang1(u1_struct_0(A), u1_lang1(A))) ) ) ).
fof(abstractness_v1_unialg_1, axiom,  (! [A] :  (l1_unialg_1(A) =>  (v1_unialg_1(A) => A=g1_unialg_1(u1_struct_0(A), u1_unialg_1(A))) ) ) ).
fof(antisymmetry_r2_hidden, axiom,  (! [A, B] :  (r2_hidden(A, B) =>  ~ (r2_hidden(B, A)) ) ) ).
fof(asymmetry_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) =>  ~ (r2_tarski(B, A)) ) ) ).
fof(cc10_card_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_zfmisc_1(A))  => v3_card_1(A, 1)) ) ).
fof(cc10_funct_2, axiom,  (! [A, B] :  (! [C] :  (m1_funct_2(C, A, B) => v4_funct_1(C)) ) ) ).
fof(cc10_membered, axiom,  (! [A] :  (v5_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_int_1(B)) ) ) ) ).
fof(cc10_ordinal1, axiom,  (! [A] :  (v6_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_ordinal1(B)) ) ) ) ).
fof(cc10_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ( ~ (v2_struct_0(A))  & v7_struct_0(A))  => v13_struct_0(A, 1)) ) ) ).
fof(cc10_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_valued_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_valued_0(B)) ) ) ) ).
fof(cc11_card_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_card_1(A))  =>  (! [B] :  (v3_card_1(B, A) =>  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(cc11_membered, axiom,  (! [A] :  (v6_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v7_ordinal1(B)) ) ) ) ).
fof(cc11_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v7_ordinal1(A)) ) ).
fof(cc11_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, 1) =>  ( ~ (v2_struct_0(A))  & v7_struct_0(A)) ) ) ) ).
fof(cc11_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v2_valued_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v2_valued_0(B)) ) ) ) ).
fof(cc12_membered, axiom,  (! [A] :  (v1_xboole_0(A) => v6_membered(A)) ) ).
fof(cc12_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v1_zfmisc_1(A)) ) ).
fof(cc12_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v3_valued_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v3_valued_0(B)) ) ) ) ).
fof(cc13_membered, axiom,  (! [A] :  (v1_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_membered(B)) ) ) ) ).
fof(cc13_ordinal1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  ~ (v8_ordinal1(A)) ) ) ).
fof(cc13_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v4_valued_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_valued_0(B)) ) ) ) ).
fof(cc14_membered, axiom,  (! [A] :  (v2_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v2_membered(B)) ) ) ) ).
fof(cc14_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc14_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_valued_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v5_valued_0(B)) ) ) ) ).
fof(cc15_card_3, axiom,  (! [A] :  ( ~ (v4_card_3(A))  =>  ~ (v1_xboole_0(A)) ) ) ).
fof(cc15_membered, axiom,  (! [A] :  (v3_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v3_membered(B)) ) ) ) ).
fof(cc15_ordinal1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v9_ordinal1(A)) ) ) ).
fof(cc15_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v6_valued_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_valued_0(B)) ) ) ) ).
fof(cc16_membered, axiom,  (! [A] :  (v4_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_membered(B)) ) ) ) ).
fof(cc16_ordinal1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) )  =>  (! [B] :  (m1_subset_1(B, A) =>  ~ (v8_ordinal1(B)) ) ) ) ) ).
fof(cc16_valued_0, axiom,  (! [A, B] :  (v1_membered(B) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_valued_0(C)) ) ) ) ).
fof(cc17_membered, axiom,  (! [A] :  (v5_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v5_membered(B)) ) ) ) ).
fof(cc17_ordinal1, axiom,  (! [A] :  ( ~ (v10_ordinal1(A))  => v1_setfam_1(A)) ) ).
fof(cc17_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc17_valued_0, axiom,  (! [A, B] :  (v2_membered(B) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v2_valued_0(C)) ) ) ) ).
fof(cc18_membered, axiom,  (! [A] :  (v6_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_membered(B)) ) ) ) ).
fof(cc18_ordinal1, axiom,  (! [A] :  (v10_ordinal1(A) =>  ~ (v1_setfam_1(A)) ) ) ).
fof(cc18_valued_0, axiom,  (! [A, B] :  (v3_membered(B) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v3_valued_0(C)) ) ) ) ).
fof(cc19_membered, axiom,  (! [A] :  (v1_xboole_0(A) => v7_membered(A)) ) ).
fof(cc19_ordinal1, axiom,  (! [A] :  (v1_setfam_1(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc19_valued_0, axiom,  (! [A, B] :  (v4_membered(B) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v4_valued_0(C)) ) ) ) ).
fof(cc1_abian, axiom,  (! [A] :  (v2_setfam_1(A) => v1_zfmisc_1(A)) ) ).
fof(cc1_aofa_000, axiom,  (! [A, B] :  ( ( ( ~ (v1_xboole_0(A))  & m1_finseq_1(A, k4_ordinal1))  &  ( ~ (v1_xboole_0(B))  & v1_freealg(B)) )  =>  (! [C] :  (m1_subset_1(C, u1_struct_0(k7_freealg(A, B))) =>  (v1_relat_1(C) & v1_funct_1(C)) ) ) ) ) ).
fof(cc1_card_1, axiom,  (! [A] :  (v1_card_1(A) => v3_ordinal1(A)) ) ).
fof(cc1_card_3, axiom,  (! [A] :  ( (v1_xboole_0(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v1_card_3(A)) ) ) ) ).
fof(cc1_finset_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_finset_1(A)) ) ).
fof(cc1_funcop_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  ( (v1_relat_1(B) &  (v5_relat_1(B, A) & v1_funct_1(B)) )  =>  (v1_relat_1(B) &  (v1_funct_1(B) & v1_funcop_1(B)) ) ) ) ) ) ).
fof(cc1_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_funct_1(A)) ) ).
fof(cc1_funct_2, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v1_partfun1(C, A) => v1_funct_2(C, A, B)) ) ) ) ).
fof(cc1_int_1, axiom,  (! [A] :  (m1_subset_1(A, k4_numbers) => v1_int_1(A)) ) ).
fof(cc1_membered, axiom,  (! [A] :  (v6_membered(A) => v5_membered(A)) ) ).
fof(cc1_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v3_ordinal1(A) & v7_ordinal1(A)) ) ) ).
fof(cc1_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (v1_ordinal1(A) & v2_ordinal1(A)) ) ) ).
fof(cc1_relset_1, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_relat_1(C)) ) ) ).
fof(cc1_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v7_struct_0(A)) ) ) ).
fof(cc1_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v6_valued_0(A))  =>  (v1_relat_1(A) & v5_valued_0(A)) ) ) ).
fof(cc1_xcmplx_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xcmplx_0(A)) ) ).
fof(cc1_xreal_0, axiom,  (! [A] :  (m1_subset_1(A, k1_numbers) => v1_xreal_0(A)) ) ).
fof(cc1_xxreal_0, axiom,  (! [A] :  (m1_subset_1(A, k6_numbers) => v1_xxreal_0(A)) ) ).
fof(cc20_ordinal1, axiom,  (! [A] :  ( ~ (v1_setfam_1(A))  => v10_ordinal1(A)) ) ).
fof(cc20_valued_0, axiom,  (! [A, B] :  (v5_membered(B) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v5_valued_0(C)) ) ) ) ).
fof(cc21_valued_0, axiom,  (! [A, B] :  (v6_membered(B) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v6_valued_0(C)) ) ) ) ).
fof(cc22_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v1_zfmisc_1(A) & v2_valued_0(A)) ) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) &  (v7_valued_0(A) & v8_valued_0(A)) ) ) ) ) ) ).
fof(cc23_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) & v7_valued_0(A)) ) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) & v9_valued_0(A)) ) ) ) ) ).
fof(cc24_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) & v8_valued_0(A)) ) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) & v10_valued_0(A)) ) ) ) ) ).
fof(cc28_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_relat_1(A, k2_numbers))  =>  (v1_relat_1(A) & v1_valued_0(A)) ) ) ).
fof(cc29_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_valued_0(A))  =>  (v1_relat_1(A) & v5_relat_1(A, k2_numbers)) ) ) ).
fof(cc2_aofa_000, axiom,  (! [A, B] :  ( ( ( ~ (v1_xboole_0(A))  & m1_finseq_1(A, k4_ordinal1))  &  ( ~ (v1_xboole_0(B))  & v1_freealg(B)) )  =>  (! [C] :  (m1_subset_1(C, u1_struct_0(k7_freealg(A, B))) => v3_trees_2(C)) ) ) ) ).
fof(cc2_card_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_card_1(A)) ) ).
fof(cc2_card_3, axiom,  (! [A, B] :  (v1_setfam_1(B) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  ( (v1_funct_1(C) & v1_funct_2(C, A, B))  =>  (v2_relat_1(C) &  (v1_funct_1(C) & v1_funct_2(C, A, B)) ) ) ) ) ) ) ).
fof(cc2_finset_1, axiom,  (! [A] :  (v1_finset_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_finset_1(B)) ) ) ) ).
fof(cc2_funcop_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funcop_1(A)) ) ) ) ).
fof(cc2_funct_1, axiom,  (! [A] :  ( (v1_xboole_0(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) ) ) ) ).
fof(cc2_funct_2, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v1_funct_2(C, A, B) => v1_partfun1(C, A)) ) ) ) ) ).
fof(cc2_int_1, axiom,  (! [A] :  (v7_ordinal1(A) => v1_int_1(A)) ) ).
fof(cc2_membered, axiom,  (! [A] :  (v5_membered(A) => v4_membered(A)) ) ).
fof(cc2_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v7_ordinal1(A) &  ~ (v3_xxreal_0(A)) ) ) ) ).
fof(cc2_ordinal1, axiom,  (! [A] :  ( (v1_ordinal1(A) & v2_ordinal1(A))  => v3_ordinal1(A)) ) ).
fof(cc2_relset_1, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ).
fof(cc2_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc2_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_valued_0(A))  =>  (v1_relat_1(A) & v4_valued_0(A)) ) ) ).
fof(cc2_xcmplx_0, axiom,  (! [A] :  (m1_subset_1(A, k1_numbers) => v1_xcmplx_0(A)) ) ).
fof(cc2_xreal_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xreal_0(A)) ) ).
fof(cc2_xxreal_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xxreal_0(A)) ) ).
fof(cc30_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_relat_1(A, k6_numbers))  =>  (v1_relat_1(A) & v2_valued_0(A)) ) ) ).
fof(cc31_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v2_valued_0(A))  =>  (v1_relat_1(A) & v5_relat_1(A, k6_numbers)) ) ) ).
fof(cc32_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_relat_1(A, k1_numbers))  =>  (v1_relat_1(A) & v3_valued_0(A)) ) ) ).
fof(cc33_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v3_valued_0(A))  =>  (v1_relat_1(A) & v5_relat_1(A, k1_numbers)) ) ) ).
fof(cc34_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_relat_1(A, k3_numbers))  =>  (v1_relat_1(A) & v4_valued_0(A)) ) ) ).
fof(cc35_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v4_valued_0(A))  =>  (v1_relat_1(A) & v5_relat_1(A, k3_numbers)) ) ) ).
fof(cc36_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_relat_1(A, k4_numbers))  =>  (v1_relat_1(A) & v5_valued_0(A)) ) ) ).
fof(cc37_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_valued_0(A))  =>  (v1_relat_1(A) & v5_relat_1(A, k4_numbers)) ) ) ).
fof(cc38_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_relat_1(A, k4_ordinal1))  =>  (v1_relat_1(A) & v6_valued_0(A)) ) ) ).
fof(cc39_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v6_valued_0(A))  =>  (v1_relat_1(A) & v5_relat_1(A, k4_ordinal1)) ) ) ).
fof(cc3_aofa_000, axiom,  (! [A, B] :  ( ( ( ~ (v1_xboole_0(A))  & m1_finseq_1(A, k4_ordinal1))  &  ( ~ (v1_xboole_0(B))  & v1_freealg(B)) )  =>  (! [C] :  (m1_finseq_1(C, u1_struct_0(k7_freealg(A, B))) => v6_trees_3(C)) ) ) ) ).
fof(cc3_card_1, axiom,  (! [A] :  (v7_ordinal1(A) => v1_card_1(A)) ) ).
fof(cc3_finset_1, axiom,  (! [A, B] :  (v1_finset_1(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  ( (v1_funct_1(C) & v1_funct_2(C, A, B))  =>  (v1_funct_1(C) &  (v1_funct_2(C, A, B) & v1_finset_1(C)) ) ) ) ) ) ) ).
fof(cc3_funcop_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_xboole_0(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) ) ) ) ).
fof(cc3_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_funct_1(B)) ) ) ) ).
fof(cc3_funct_2, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v1_funct_2(C, A, B) => v1_partfun1(C, A)) ) ) ) ) ).
fof(cc3_int_1, axiom,  (! [A] :  (v1_int_1(A) => v1_xreal_0(A)) ) ).
fof(cc3_membered, axiom,  (! [A] :  (v4_membered(A) => v3_membered(A)) ) ).
fof(cc3_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v7_ordinal1(A) &  ~ (v3_xxreal_0(A)) ) ) ) ).
fof(cc3_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_ordinal1(A)) ) ).
fof(cc3_relset_1, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_xboole_0(C)) ) ) ) ).
fof(cc3_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_valued_0(A))  =>  (v1_relat_1(A) & v3_valued_0(A)) ) ) ).
fof(cc3_xcmplx_0, axiom,  (! [A] :  (m1_subset_1(A, k2_numbers) => v1_xcmplx_0(A)) ) ).
fof(cc3_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xcmplx_0(A)) ) ).
fof(cc3_xxreal_0, axiom,  (! [A] :  ( (v1_xxreal_0(A) & v2_xxreal_0(A))  =>  ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v3_xxreal_0(A)) ) ) ) ) ).
fof(cc40_valued_0, axiom,  (! [A] :  (v1_membered(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_relat_1(B) & v5_relat_1(B, k2_numbers)) ) ) ) ) ).
fof(cc41_valued_0, axiom,  (! [A] :  (v1_membered(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_relat_1(B) & v1_valued_0(B)) ) ) ) ) ).
fof(cc42_valued_0, axiom,  (! [A] :  (v2_membered(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_relat_1(B) & v5_relat_1(B, k6_numbers)) ) ) ) ) ).
fof(cc43_valued_0, axiom,  (! [A] :  (v2_membered(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_relat_1(B) & v2_valued_0(B)) ) ) ) ) ).
fof(cc44_valued_0, axiom,  (! [A] :  (v3_membered(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_relat_1(B) & v5_relat_1(B, k1_numbers)) ) ) ) ) ).
fof(cc45_valued_0, axiom,  (! [A] :  (v3_membered(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_relat_1(B) & v3_valued_0(B)) ) ) ) ) ).
fof(cc46_valued_0, axiom,  (! [A] :  (v4_membered(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_relat_1(B) & v5_relat_1(B, k3_numbers)) ) ) ) ) ).
fof(cc47_valued_0, axiom,  (! [A] :  (v4_membered(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_relat_1(B) & v4_valued_0(B)) ) ) ) ) ).
fof(cc48_valued_0, axiom,  (! [A] :  (v5_membered(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_relat_1(B) & v5_relat_1(B, k4_numbers)) ) ) ) ) ).
fof(cc49_valued_0, axiom,  (! [A] :  (v5_membered(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_relat_1(B) & v5_valued_0(B)) ) ) ) ) ).
fof(cc4_aofa_000, axiom,  (! [A] :  (l1_unialg_1(A) =>  ( ( ~ (v2_struct_0(A))  &  (v2_unialg_1(A) &  (v3_unialg_1(A) &  (v4_unialg_1(A) &  (v3_freealg(A) &  (v3_aofa_000(A) &  (v4_aofa_000(A) &  (v5_aofa_000(A) & v6_aofa_000(A)) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  (v2_unialg_1(A) &  (v3_unialg_1(A) &  (v4_unialg_1(A) &  (v3_aofa_000(A) &  (v4_aofa_000(A) &  (v5_aofa_000(A) &  (v6_aofa_000(A) &  ( ~ (v10_aofa_000(A))  & v11_aofa_000(A)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(cc4_card_1, axiom,  (! [A] :  (m1_subset_1(A, k4_ordinal1) => v1_finset_1(A)) ) ).
fof(cc4_card_3, axiom,  (! [A] :  (v5_card_3(A) =>  ( ~ (v1_finset_1(A))  & v4_card_3(A)) ) ) ).
fof(cc4_finset_1, axiom,  (! [A] :  (v1_zfmisc_1(A) => v1_finset_1(A)) ) ).
fof(cc4_funcop_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(B))  &  ~ (v1_xboole_0(C)) )  =>  (! [D] :  (m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(B, k9_funct_2(A, C)))) =>  ( (v1_funct_1(D) & v1_funct_2(D, B, k9_funct_2(A, C)))  =>  (v1_funct_1(D) &  (v1_funct_2(D, B, k9_funct_2(A, C)) & v1_funcop_1(D)) ) ) ) ) ) ) ).
fof(cc4_funct_1, axiom,  (! [A] :  ( (v1_xboole_0(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) ) ) ) ).
fof(cc4_funct_2, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, A))) =>  (v1_funct_2(B, A, A) => v1_partfun1(B, A)) ) ) ) ).
fof(cc4_int_1, axiom,  (! [A] :  (v7_ordinal1(A) => v2_int_1(A)) ) ).
fof(cc4_membered, axiom,  (! [A] :  (v3_membered(A) => v2_membered(A)) ) ).
fof(cc4_nat_1, axiom,  (! [A] :  ( (v7_ordinal1(A) & v8_ordinal1(A))  =>  (v7_ordinal1(A) &  ~ (v2_xxreal_0(A)) ) ) ) ).
fof(cc4_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v5_ordinal1(A)) ) ).
fof(cc4_relset_1, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A))) => v1_xboole_0(C)) ) ) ) ).
fof(cc4_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) =>  (v2_struct_0(A) & v8_struct_0(A)) ) ) ) ).
fof(cc4_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v4_valued_0(A))  =>  (v1_relat_1(A) & v3_valued_0(A)) ) ) ).
fof(cc4_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xxreal_0(A)) ) ).
fof(cc4_xxreal_0, axiom,  (! [A] :  ( ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v3_xxreal_0(A)) ) )  =>  (v1_xxreal_0(A) & v2_xxreal_0(A)) ) ) ).
fof(cc50_valued_0, axiom,  (! [A] :  (v6_membered(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_relat_1(B) & v5_relat_1(B, k4_ordinal1)) ) ) ) ) ).
fof(cc51_valued_0, axiom,  (! [A] :  (v6_membered(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_relat_1(B) & v6_valued_0(B)) ) ) ) ) ).
fof(cc5_aofa_000, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_unialg_1(A) &  (v3_unialg_1(A) &  (v4_unialg_1(A) &  (v3_aofa_000(A) &  (v4_aofa_000(A) &  (v5_aofa_000(A) &  (v6_aofa_000(A) & l1_unialg_1(A)) ) ) ) ) ) ) )  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(C, k1_zfmisc_1(B))) )  =>  (! [D] :  (m1_aofa_000(D, A, B, C) =>  (v13_aofa_000(D, A, B) & v14_aofa_000(D, A, B)) ) ) ) ) ).
fof(cc5_card_1, axiom,  (! [A] :  (v7_ordinal1(A) => v1_finset_1(A)) ) ).
fof(cc5_card_3, axiom,  (! [A] :  ( ( ~ (v1_finset_1(A))  & v4_card_3(A))  => v5_card_3(A)) ) ).
fof(cc5_finset_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  ~ (v1_zfmisc_1(A)) ) ) ).
fof(cc5_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) )  =>  ( ~ (v1_zfmisc_1(A))  &  (v1_relat_1(A) & v1_funct_1(A)) ) ) ) ).
fof(cc5_funct_2, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A))) =>  (v1_funct_2(B, k2_zfmisc_1(A, A), A) => v1_partfun1(B, k2_zfmisc_1(A, A))) ) ) ) ).
fof(cc5_int_1, axiom,  (! [A] :  (v2_int_1(A) => v1_int_1(A)) ) ).
fof(cc5_membered, axiom,  (! [A] :  (v3_membered(A) => v1_membered(A)) ) ).
fof(cc5_nat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v8_ordinal1(A)) ) ).
fof(cc5_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, A) => v3_ordinal1(B)) ) ) ) ).
fof(cc5_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ( ~ (v2_struct_0(A))  &  ~ (v8_struct_0(A)) ) ) ) ) ).
fof(cc5_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v3_valued_0(A))  =>  (v1_relat_1(A) & v2_valued_0(A)) ) ) ).
fof(cc5_xxreal_0, axiom,  (! [A] :  ( (v1_xxreal_0(A) & v3_xxreal_0(A))  =>  ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v2_xxreal_0(A)) ) ) ) ) ).
fof(cc6_card_1, axiom,  (! [A] :  ( (v3_ordinal1(A) & v1_finset_1(A))  => v7_ordinal1(A)) ) ).
fof(cc6_card_3, axiom,  (! [A] :  (v1_finset_1(A) => v4_card_3(A)) ) ).
fof(cc6_finset_1, axiom,  (! [A] :  (v1_xboole_0(A) => v5_finset_1(A)) ) ).
fof(cc6_funct_1, axiom,  (! [A] :  ( (v1_zfmisc_1(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) ) ) ) ).
fof(cc6_membered, axiom,  (! [A] :  (v1_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xcmplx_0(B)) ) ) ) ).
fof(cc6_nat_1, axiom,  (! [A] :  ( ~ (v8_ordinal1(A))  =>  ~ (v1_xboole_0(A)) ) ) ).
fof(cc6_ordinal1, axiom,  (! [A] :  (v7_ordinal1(A) => v3_ordinal1(A)) ) ).
fof(cc6_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v7_struct_0(A) => v8_struct_0(A)) ) ) ).
fof(cc6_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v3_valued_0(A))  =>  (v1_relat_1(A) & v1_valued_0(A)) ) ) ).
fof(cc6_xxreal_0, axiom,  (! [A] :  ( ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v2_xxreal_0(A)) ) )  =>  (v1_xxreal_0(A) & v3_xxreal_0(A)) ) ) ).
fof(cc7_card_1, axiom,  (! [A] :  (v3_card_1(A, k5_ordinal1) => v1_xboole_0(A)) ) ).
fof(cc7_card_3, axiom,  (! [A] :  (v4_card_3(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_card_3(B)) ) ) ) ).
fof(cc7_finset_1, axiom,  (! [A] :  (v5_finset_1(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_finset_1(B)) ) ) ) ).
fof(cc7_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v4_funct_1(A)) ) ).
fof(cc7_membered, axiom,  (! [A] :  (v2_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xxreal_0(B)) ) ) ) ).
fof(cc7_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v7_ordinal1(A)) ) ).
fof(cc7_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ~ (v7_struct_0(A)) ) ) ) ).
fof(cc7_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v6_valued_0(A))  =>  (v1_relat_1(A) & v4_valued_0(A)) ) ) ).
fof(cc7_xxreal_0, axiom,  (! [A] :  ( (v8_ordinal1(A) & v1_xxreal_0(A))  =>  (v1_xxreal_0(A) &  ( ~ (v2_xxreal_0(A))  &  ~ (v3_xxreal_0(A)) ) ) ) ) ).
fof(cc8_card_1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_card_1(A, k5_ordinal1)) ) ).
fof(cc8_card_3, axiom,  (! [A] :  (v2_card_3(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v2_card_3(B)) ) ) ) ).
fof(cc8_finset_1, axiom,  (! [A] :  (v5_finset_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v5_finset_1(B)) ) ) ) ).
fof(cc8_funct_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  (m1_subset_1(B, A) =>  (v1_relat_1(B) & v1_funct_1(B)) ) ) ) ) ).
fof(cc8_membered, axiom,  (! [A] :  (v3_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xreal_0(B)) ) ) ) ).
fof(cc8_ordinal1, axiom,  (! [A] :  (m1_subset_1(A, k4_ordinal1) => v7_ordinal1(A)) ) ).
fof(cc8_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v13_struct_0(A, k5_ordinal1)) ) ) ).
fof(cc8_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v6_valued_0(A))  =>  (v1_relat_1(A) & v3_valued_0(A)) ) ) ).
fof(cc8_xxreal_0, axiom,  (! [A] :  ( (v1_xxreal_0(A) &  ( ~ (v2_xxreal_0(A))  &  ~ (v3_xxreal_0(A)) ) )  =>  (v8_ordinal1(A) & v1_xxreal_0(A)) ) ) ).
fof(cc9_card_1, axiom,  (! [A] :  (v3_card_1(A, 1) =>  ( ~ (v1_xboole_0(A))  & v1_zfmisc_1(A)) ) ) ).
fof(cc9_finset_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v2_finset_1(A)) ) ) ).
fof(cc9_funct_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_funct_1(B)) ) ) ) ).
fof(cc9_funct_2, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  ( (v1_funct_1(C) & v1_funct_2(C, A, B))  =>  (v1_funct_1(C) &  ( ~ (v1_xboole_0(C))  & v1_funct_2(C, A, B)) ) ) ) ) ) ) ).
fof(cc9_membered, axiom,  (! [A] :  (v4_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_rat_1(B)) ) ) ) ).
fof(cc9_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v6_ordinal1(A)) ) ).
fof(cc9_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, k5_ordinal1) => v2_struct_0(A)) ) ) ).
fof(cc9_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_xboole_0(A))  =>  (v1_relat_1(A) & v6_valued_0(A)) ) ) ).
fof(commutativity_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, B)=k2_xboole_0(B, A)) ).
fof(d12_freealg, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & m2_finseq_1(A, k4_ordinal1))  =>  (! [B] :  ( ( ~ (v1_xboole_0(B))  & v1_freealg(B))  => k7_freealg(A, B)=g1_unialg_1(k4_dtconstr(k3_freealg(A, B)), k6_freealg(A, B))) ) ) ) ).
fof(d13_freealg, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & m2_finseq_1(A, k4_ordinal1))  =>  (! [B] :  ( ( ~ (v1_xboole_0(B))  & v1_freealg(B))  => k8_freealg(A, B)=a_2_0_freealg(A, B)) ) ) ) ).
fof(d14_aofa_i00, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_unialg_1(A) &  (v3_unialg_1(A) &  (v4_unialg_1(A) &  (v3_aofa_000(A) &  (v4_aofa_000(A) &  (v5_aofa_000(A) &  (v6_aofa_000(A) & l1_unialg_1(A)) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  ( ~ (v1_xboole_0(C))  =>  (! [D] :  (m1_subset_1(D, k1_zfmisc_1(k9_funct_2(C, k4_numbers))) =>  (! [E] :  (m1_aofa_000(E, A, k9_funct_2(C, k4_numbers), D) =>  (r1_aofa_i00(A, B, C, D, E) <=>  (r2_tarski(B, k18_aofa_000(A)) &  (? [F] :  ( (v1_funct_1(F) &  (v1_funct_2(F, k9_funct_2(C, k4_numbers), C) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(k9_funct_2(C, k4_numbers), C)))) )  &  (? [G] :  ( (v1_funct_1(G) &  (v1_funct_2(G, k9_funct_2(C, k4_numbers), k4_numbers) & m1_subset_1(G, k1_zfmisc_1(k2_zfmisc_1(k9_funct_2(C, k4_numbers), k4_numbers)))) )  &  (! [H] :  (m2_funct_2(H, C, k4_numbers, k9_funct_2(C, k4_numbers)) => k2_binop_1(k9_funct_2(C, k4_numbers), u1_struct_0(A), k9_funct_2(C, k4_numbers), E, H, B)=k14_funct_7(C, k4_numbers, H, k3_funct_2(k9_funct_2(C, k4_numbers), C, F, H), k3_funct_2(k9_funct_2(C, k4_numbers), k4_numbers, G, H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d15_aofa_i00, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_unialg_1(A) &  (v3_unialg_1(A) &  (v4_unialg_1(A) &  (v3_aofa_000(A) &  (v4_aofa_000(A) &  (v5_aofa_000(A) &  (v6_aofa_000(A) & l1_unialg_1(A)) ) ) ) ) ) ) )  =>  (! [B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k9_funct_2(B, k4_numbers))) =>  (! [D] :  (m1_aofa_000(D, A, k9_funct_2(B, k4_numbers), C) =>  (! [E] :  ( (v1_funct_1(E) &  (v1_funct_2(E, k9_funct_2(B, k4_numbers), B) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(k9_funct_2(B, k4_numbers), B)))) )  =>  (! [F] :  ( (v1_funct_1(F) &  (v1_funct_2(F, k9_funct_2(B, k4_numbers), k4_numbers) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(k9_funct_2(B, k4_numbers), k4_numbers)))) )  =>  (r2_aofa_i00(A, B, C, D, E, F) <=>  (? [G] :  (m1_subset_1(G, u1_struct_0(A)) &  (r2_tarski(G, k18_aofa_000(A)) &  (! [H] :  (m2_funct_2(H, B, k4_numbers, k9_funct_2(B, k4_numbers)) => k2_binop_1(k9_funct_2(B, k4_numbers), u1_struct_0(A), k9_funct_2(B, k4_numbers), D, H, G)=k14_funct_7(B, k4_numbers, H, k3_funct_2(k9_funct_2(B, k4_numbers), B, E, H), k3_funct_2(k9_funct_2(B, k4_numbers), k4_numbers, F, H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d16_aofa_000, axiom,  (! [A] :  ( (v4_unialg_1(A) &  (v3_aofa_000(A) & l1_unialg_1(A)) )  => k12_aofa_000(A)=k1_funct_1(k2_pua2mss1(A, k10_subset_1(1, k4_finseq_1(u1_unialg_1(A)))), k1_xboole_0)) ) ).
fof(d16_aofa_i00, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_unialg_1(A) &  (v3_unialg_1(A) &  (v4_unialg_1(A) &  (v3_aofa_000(A) &  (v4_aofa_000(A) &  (v5_aofa_000(A) &  (v6_aofa_000(A) & l1_unialg_1(A)) ) ) ) ) ) ) )  =>  (! [B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k9_funct_2(B, k4_numbers))) =>  (! [D] :  (m1_aofa_000(D, A, k9_funct_2(B, k4_numbers), C) =>  ( (? [E] :  (m1_subset_1(E, u1_struct_0(A)) & r1_aofa_i00(A, E, B, C, D)) )  =>  (! [E] :  ( (v1_funct_1(E) &  (v1_funct_2(E, k9_funct_2(B, k4_numbers), B) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(k9_funct_2(B, k4_numbers), B)))) )  =>  (m2_aofa_i00(E, A, B, C, D) <=>  (? [F] :  ( (v1_funct_1(F) &  (v1_funct_2(F, k9_funct_2(B, k4_numbers), k4_numbers) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(k9_funct_2(B, k4_numbers), k4_numbers)))) )  & r2_aofa_i00(A, B, C, D, E, F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d17_aofa_000, axiom,  (! [A] :  ( (v4_unialg_1(A) &  (v4_aofa_000(A) & l1_unialg_1(A)) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => k13_aofa_000(A, B, C)=k1_funct_1(k2_pua2mss1(A, k10_subset_1(2, k4_finseq_1(u1_unialg_1(A)))), k2_finseq_4(u1_struct_0(A), B, C))) ) ) ) ) ) ).
fof(d1_aofa_i00, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v4_funct_1(A))  =>  (! [B] :  (! [C] : k1_aofa_i00(A, B, C)=a_3_0_aofa_i00(A, B, C)) ) ) ) ).
fof(d1_binop_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  (! [C] : k1_binop_1(A, B, C)=k1_funct_1(A, k4_tarski(B, C))) ) ) ) ).
fof(d22_aofa_000, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_unialg_1(A) &  (v3_unialg_1(A) &  (v4_unialg_1(A) &  (v3_aofa_000(A) &  (v4_aofa_000(A) &  (v5_aofa_000(A) &  (v6_aofa_000(A) & l1_unialg_1(A)) ) ) ) ) ) ) )  => k18_aofa_000(A)=k7_subset_1(u1_struct_0(A), k7_subset_1(u1_struct_0(A), k7_subset_1(u1_struct_0(A), k6_subset_1(u1_struct_0(A), k1_tarski(k12_aofa_000(A))), k2_relset_1(u1_struct_0(A), k2_pua2mss1(A, k10_subset_1(3, k4_finseq_1(u1_unialg_1(A)))))), k2_relset_1(u1_struct_0(A), k2_pua2mss1(A, k10_subset_1(4, k4_finseq_1(u1_unialg_1(A)))))), a_1_1_aofa_000(A))) ) ).
fof(d24_aofa_i00, axiom, k26_aofa_i00=k2_zfmisc_1(k9_funct_2(k9_funct_2(k4_ordinal1, k4_numbers), k4_ordinal1), k9_funct_2(k9_funct_2(k4_ordinal1, k4_numbers), k4_numbers))).
fof(d25_aofa_i00, axiom,  (! [A] :  (m1_aofa_000(A, k7_freealg(k19_aofa_000, k26_aofa_i00), k9_funct_2(k4_ordinal1, k4_numbers), k1_aofa_i00(k9_funct_2(k4_ordinal1, k4_numbers), k5_numbers, k5_numbers)) =>  (m4_aofa_i00(A) <=>  (! [B] :  (m2_funct_2(B, k4_ordinal1, k4_numbers, k9_funct_2(k4_ordinal1, k4_numbers)) =>  (! [C] :  (m2_funct_2(C, k9_funct_2(k4_ordinal1, k4_numbers), k4_ordinal1, k9_funct_2(k9_funct_2(k4_ordinal1, k4_numbers), k4_ordinal1)) =>  (! [D] :  (m2_funct_2(D, k9_funct_2(k4_ordinal1, k4_numbers), k4_numbers, k9_funct_2(k9_funct_2(k4_ordinal1, k4_numbers), k4_numbers)) => k1_binop_1(A, B, k1_trees_4(k4_tarski(C, D)))=k14_funct_7(k4_ordinal1, k4_numbers, B, k21_aofa_i00(k9_funct_2(k4_ordinal1, k4_numbers), k4_ordinal1, C, B), k21_aofa_i00(k9_funct_2(k4_ordinal1, k4_numbers), k4_numbers, D, B))) ) ) ) ) ) ) ) ) ).
fof(d26_aofa_000, axiom, k19_aofa_000=k8_finseq_1(k4_ordinal1, k2_finseq_4(k4_ordinal1, k5_numbers, 2), k2_finseq_4(k4_ordinal1, 3, 2))).
fof(d8_freealg, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & m2_finseq_1(A, k4_ordinal1))  =>  (! [B] : k3_freealg(A, B)=g1_lang1(k2_xboole_0(k4_finseq_1(A), B), k2_freealg(A, B))) ) ) ).
fof(dt_g1_lang1, axiom,  (! [A, B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k3_finseq_2(A)))) =>  (v1_lang1(g1_lang1(A, B)) & l1_lang1(g1_lang1(A, B))) ) ) ).
fof(dt_g1_unialg_1, axiom,  (! [A, B] :  (m1_finseq_1(B, k4_partfun1(k3_finseq_2(A), A)) =>  (v1_unialg_1(g1_unialg_1(A, B)) & l1_unialg_1(g1_unialg_1(A, B))) ) ) ).
fof(dt_k10_finseq_1, axiom, $true).
fof(dt_k10_subset_1, axiom,  (! [A, B] : m1_subset_1(k10_subset_1(A, B), B)) ).
fof(dt_k10_xtuple_0, axiom, $true).
fof(dt_k12_aofa_000, axiom,  (! [A] :  ( (v4_unialg_1(A) &  (v3_aofa_000(A) & l1_unialg_1(A)) )  => m1_subset_1(k12_aofa_000(A), u1_struct_0(A))) ) ).
fof(dt_k12_freealg, axiom,  (! [A, B] :  ( ( ( ~ (v1_xboole_0(A))  & m1_finseq_1(A, k4_ordinal1))  &  ( ~ (v1_xboole_0(B))  & v1_freealg(B)) )  =>  (v2_freealg(k12_freealg(A, B), k7_freealg(A, B)) & m1_freealg(k12_freealg(A, B), k7_freealg(A, B))) ) ) ).
fof(dt_k13_aofa_000, axiom,  (! [A, B, C] :  ( ( (v4_unialg_1(A) &  (v4_aofa_000(A) & l1_unialg_1(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k13_aofa_000(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k13_finseq_1, axiom, $true).
fof(dt_k14_funct_7, axiom,  (! [A, B, C, D, E] :  ( ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  & m1_subset_1(E, B))  =>  (v1_funct_1(k14_funct_7(A, B, C, D, E)) &  (v1_funct_2(k14_funct_7(A, B, C, D, E), A, B) & m1_subset_1(k14_funct_7(A, B, C, D, E), k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) ) ) ).
fof(dt_k18_aofa_000, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_unialg_1(A) &  (v3_unialg_1(A) &  (v4_unialg_1(A) &  (v3_aofa_000(A) &  (v4_aofa_000(A) &  (v5_aofa_000(A) &  (v6_aofa_000(A) & l1_unialg_1(A)) ) ) ) ) ) ) )  => m1_subset_1(k18_aofa_000(A), k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k19_aofa_000, axiom,  ( ~ (v1_xboole_0(k19_aofa_000))  & m2_finseq_1(k19_aofa_000, k4_ordinal1)) ).
fof(dt_k1_aofa_i00, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  & v4_funct_1(A))  => m1_subset_1(k1_aofa_i00(A, B, C), k1_zfmisc_1(A))) ) ).
fof(dt_k1_binop_1, axiom, $true).
fof(dt_k1_card_1, axiom,  (! [A] : v1_card_1(k1_card_1(A))) ).
fof(dt_k1_funct_1, axiom, $true).
fof(dt_k1_funct_2, axiom, $true).
fof(dt_k1_funct_7, axiom,  (! [A, B, C] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (v1_relat_1(k1_funct_7(A, B, C)) & v1_funct_1(k1_funct_7(A, B, C))) ) ) ).
fof(dt_k1_lang1, axiom, $true).
fof(dt_k1_numbers, axiom, $true).
fof(dt_k1_pua2mss1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_finseq_1(B, k4_partfun1(k3_finseq_2(A), A)))  => m1_subset_1(k1_pua2mss1(A, B), k1_zfmisc_1(k4_partfun1(k3_finseq_2(A), A)))) ) ).
fof(dt_k1_tarski, axiom, $true).
fof(dt_k1_trees_4, axiom,  (! [A] :  (v1_relat_1(k1_trees_4(A)) &  (v1_funct_1(k1_trees_4(A)) & v3_trees_2(k1_trees_4(A))) ) ) ).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k21_aofa_i00, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  (m1_subset_1(C, k9_funct_2(A, B)) & m1_subset_1(D, A)) ) )  => m1_subset_1(k21_aofa_i00(A, B, C, D), B)) ) ).
fof(dt_k26_aofa_i00, axiom,  ( ~ (v1_finset_1(k26_aofa_i00))  & v1_freealg(k26_aofa_i00)) ).
fof(dt_k2_binop_1, axiom,  (! [A, B, C, D, E, F] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( (v1_funct_1(D) &  (v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, B), C)))) )  &  (m1_subset_1(E, A) & m1_subset_1(F, B)) ) ) )  => m1_subset_1(k2_binop_1(A, B, C, D, E, F), C)) ) ).
fof(dt_k2_finseq_4, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  (m1_subset_1(B, A) & m1_subset_1(C, A)) )  => m2_finseq_1(k2_finseq_4(A, B, C), A)) ) ).
fof(dt_k2_freealg, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_finseq_1(A, k4_ordinal1))  => m1_subset_1(k2_freealg(A, B), k1_zfmisc_1(k2_zfmisc_1(k2_xboole_0(k4_finseq_1(A), B), k3_finseq_2(k2_xboole_0(k4_finseq_1(A), B)))))) ) ).
fof(dt_k2_numbers, axiom, $true).
fof(dt_k2_pua2mss1, axiom,  (! [A, B] :  ( ( (v4_unialg_1(A) & l1_unialg_1(A))  & m1_subset_1(B, k4_finseq_1(u1_unialg_1(A))))  => m1_pua2mss1(k2_pua2mss1(A, B), k3_finseq_2(u1_struct_0(A)), u1_struct_0(A), k1_pua2mss1(u1_struct_0(A), u1_unialg_1(A)))) ) ).
fof(dt_k2_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  => m1_subset_1(k2_relset_1(A, B), k1_zfmisc_1(A))) ) ).
fof(dt_k2_trees_4, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(B, A))  => m1_subset_1(k2_trees_4(A, B), k5_trees_3(A))) ) ).
fof(dt_k2_xboole_0, axiom, $true).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_finseq_2, axiom,  (! [A] : m1_finseq_2(k3_finseq_2(A), A)) ).
fof(dt_k3_freealg, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_finseq_1(A, k4_ordinal1))  =>  (v1_lang1(k3_freealg(A, B)) & l1_lang1(k3_freealg(A, B))) ) ) ).
fof(dt_k3_funct_2, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  & m1_subset_1(D, A)) )  => m1_subset_1(k3_funct_2(A, B, C, D), B)) ) ).
fof(dt_k3_numbers, axiom, $true).
fof(dt_k4_dtconstr, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_lang1(A))  => m1_subset_1(k4_dtconstr(A), k1_zfmisc_1(k5_trees_3(u1_struct_0(A))))) ) ).
fof(dt_k4_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  => m1_subset_1(k4_finseq_1(A), k1_zfmisc_1(k4_ordinal1))) ) ).
fof(dt_k4_numbers, axiom, $true).
fof(dt_k4_ordinal1, axiom, $true).
fof(dt_k4_partfun1, axiom, $true).
fof(dt_k4_tarski, axiom, $true).
fof(dt_k4_xboole_0, axiom, $true).
fof(dt_k5_numbers, axiom, m1_subset_1(k5_numbers, k4_ordinal1)).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k5_trees_3, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  => m1_trees_3(k5_trees_3(A), A)) ) ).
fof(dt_k6_dtconstr, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v1_dtconstr(A) & l1_lang1(A)) )  =>  ( ~ (v1_xboole_0(k6_dtconstr(A)))  & m1_subset_1(k6_dtconstr(A), k1_zfmisc_1(u1_struct_0(A)))) ) ) ).
fof(dt_k6_freealg, axiom,  (! [A, B] :  ( ( ( ~ (v1_xboole_0(A))  & m1_finseq_1(A, k4_ordinal1))  &  ( ~ (v1_xboole_0(B))  & v1_freealg(B)) )  => m2_finseq_1(k6_freealg(A, B), k4_partfun1(k3_finseq_2(k4_dtconstr(k3_freealg(A, B))), k4_dtconstr(k3_freealg(A, B))))) ) ).
fof(dt_k6_numbers, axiom, $true).
fof(dt_k6_subset_1, axiom,  (! [A, B] : m1_subset_1(k6_subset_1(A, B), k1_zfmisc_1(A))) ).
fof(dt_k7_finseq_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) & v1_finseq_1(B)) ) )  =>  (v1_relat_1(k7_finseq_1(A, B)) &  (v1_funct_1(k7_finseq_1(A, B)) & v1_finseq_1(k7_finseq_1(A, B))) ) ) ) ).
fof(dt_k7_freealg, axiom,  (! [A, B] :  ( ( ( ~ (v1_xboole_0(A))  & m1_finseq_1(A, k4_ordinal1))  &  ( ~ (v1_xboole_0(B))  & v1_freealg(B)) )  =>  ( ~ (v2_struct_0(k7_freealg(A, B)))  &  (v1_unialg_1(k7_freealg(A, B)) &  (v2_unialg_1(k7_freealg(A, B)) &  (v3_unialg_1(k7_freealg(A, B)) &  (v4_unialg_1(k7_freealg(A, B)) & l1_unialg_1(k7_freealg(A, B))) ) ) ) ) ) ) ).
fof(dt_k7_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(B, k1_zfmisc_1(A)) => m1_subset_1(k7_subset_1(A, B, C), k1_zfmisc_1(A))) ) ).
fof(dt_k8_finseq_1, axiom,  (! [A, B, C] :  ( (m1_finseq_1(B, A) & m1_finseq_1(C, A))  => m2_finseq_1(k8_finseq_1(A, B, C), A)) ) ).
fof(dt_k8_freealg, axiom,  (! [A, B] :  ( ( ( ~ (v1_xboole_0(A))  & m1_finseq_1(A, k4_ordinal1))  &  ( ~ (v1_xboole_0(B))  & v1_freealg(B)) )  => m1_subset_1(k8_freealg(A, B), k1_zfmisc_1(u1_struct_0(k7_freealg(A, B))))) ) ).
fof(dt_k9_funct_2, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  => m1_funct_2(k9_funct_2(A, B), A, B)) ) ).
fof(dt_k9_xtuple_0, axiom, $true).
fof(dt_l1_lang1, axiom,  (! [A] :  (l1_lang1(A) => l1_struct_0(A)) ) ).
fof(dt_l1_struct_0, axiom, $true).
fof(dt_l1_unialg_1, axiom,  (! [A] :  (l1_unialg_1(A) => l1_struct_0(A)) ) ).
fof(dt_m1_aofa_000, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_unialg_1(A) &  (v3_unialg_1(A) &  (v4_unialg_1(A) &  (v3_aofa_000(A) &  (v4_aofa_000(A) &  (v5_aofa_000(A) &  (v6_aofa_000(A) & l1_unialg_1(A)) ) ) ) ) ) ) )  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(C, k1_zfmisc_1(B))) )  =>  (! [D] :  (m1_aofa_000(D, A, B, C) =>  (v1_funct_1(D) &  (v1_funct_2(D, k2_zfmisc_1(B, u1_struct_0(A)), B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(B, u1_struct_0(A)), B)))) ) ) ) ) ) ).
fof(dt_m1_finseq_1, axiom,  (! [A] :  (! [B] :  (m1_finseq_1(B, A) =>  (v1_relat_1(B) &  (v1_funct_1(B) & v1_finseq_1(B)) ) ) ) ) ).
fof(dt_m1_finseq_2, axiom, $true).
fof(dt_m1_freealg, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_unialg_1(A) &  (v3_unialg_1(A) &  (v4_unialg_1(A) & l1_unialg_1(A)) ) ) )  =>  (! [B] :  (m1_freealg(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) ) ) ) ).
fof(dt_m1_funct_2, axiom,  (! [A, B] :  (! [C] :  (m1_funct_2(C, A, B) =>  ~ (v1_xboole_0(C)) ) ) ) ).
fof(dt_m1_pua2mss1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(C))  & m1_subset_1(C, k1_zfmisc_1(k4_partfun1(A, B)))) ) )  =>  (! [D] :  (m1_pua2mss1(D, A, B, C) =>  (v1_funct_1(D) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) ) ) ) ).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_m1_trees_3, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_trees_3(B, A) =>  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(dt_m2_aofa_i00, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_unialg_1(A) &  (v3_unialg_1(A) &  (v4_unialg_1(A) &  (v3_aofa_000(A) &  (v4_aofa_000(A) &  (v5_aofa_000(A) &  (v6_aofa_000(A) & l1_unialg_1(A)) ) ) ) ) ) ) )  &  ( ~ (v1_xboole_0(B))  &  (m1_subset_1(C, k1_zfmisc_1(k9_funct_2(B, k4_numbers))) & m1_aofa_000(D, A, k9_funct_2(B, k4_numbers), C)) ) )  =>  (! [E] :  (m2_aofa_i00(E, A, B, C, D) =>  (v1_funct_1(E) &  (v1_funct_2(E, k9_funct_2(B, k4_numbers), B) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(k9_funct_2(B, k4_numbers), B)))) ) ) ) ) ) ).
fof(dt_m2_finseq_1, axiom,  (! [A] :  (! [B] :  (m2_finseq_1(B, A) =>  (v1_funct_1(B) &  (v1_finseq_1(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, A)))) ) ) ) ) ).
fof(dt_m2_funct_2, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(B))  & m1_funct_2(C, A, B))  =>  (! [D] :  (m2_funct_2(D, A, B, C) =>  (v1_funct_1(D) &  (v1_funct_2(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) ) ) ) ) ).
fof(dt_m4_aofa_i00, axiom,  (! [A] :  (m4_aofa_i00(A) => m1_aofa_000(A, k7_freealg(k19_aofa_000, k26_aofa_i00), k9_funct_2(k4_ordinal1, k4_numbers), k1_aofa_i00(k9_funct_2(k4_ordinal1, k4_numbers), k5_numbers, k5_numbers))) ) ).
fof(dt_o_0_0_aofa_i00, axiom,  (v1_funct_1(o_0_0_aofa_i00) &  (v1_funct_2(o_0_0_aofa_i00, k9_funct_2(k4_ordinal1, k4_numbers), k4_numbers) & m1_subset_1(o_0_0_aofa_i00, k1_zfmisc_1(k2_zfmisc_1(k9_funct_2(k4_ordinal1, k4_numbers), k4_numbers)))) ) ).
fof(dt_u1_lang1, axiom,  (! [A] :  (l1_lang1(A) => m1_subset_1(u1_lang1(A), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), k3_finseq_2(u1_struct_0(A)))))) ) ).
fof(dt_u1_struct_0, axiom, $true).
fof(dt_u1_unialg_1, axiom,  (! [A] :  (l1_unialg_1(A) => m2_finseq_1(u1_unialg_1(A), k4_partfun1(k3_finseq_2(u1_struct_0(A)), u1_struct_0(A)))) ) ).
fof(existence_l1_lang1, axiom,  (? [A] : l1_lang1(A)) ).
fof(existence_l1_struct_0, axiom,  (? [A] : l1_struct_0(A)) ).
fof(existence_l1_unialg_1, axiom,  (? [A] : l1_unialg_1(A)) ).
fof(existence_m1_aofa_000, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_unialg_1(A) &  (v3_unialg_1(A) &  (v4_unialg_1(A) &  (v3_aofa_000(A) &  (v4_aofa_000(A) &  (v5_aofa_000(A) &  (v6_aofa_000(A) & l1_unialg_1(A)) ) ) ) ) ) ) )  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(C, k1_zfmisc_1(B))) )  =>  (? [D] : m1_aofa_000(D, A, B, C)) ) ) ).
fof(existence_m1_finseq_1, axiom,  (! [A] :  (? [B] : m1_finseq_1(B, A)) ) ).
fof(existence_m1_finseq_2, axiom,  (! [A] :  (? [B] : m1_finseq_2(B, A)) ) ).
fof(existence_m1_freealg, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_unialg_1(A) &  (v3_unialg_1(A) &  (v4_unialg_1(A) & l1_unialg_1(A)) ) ) )  =>  (? [B] : m1_freealg(B, A)) ) ) ).
fof(existence_m1_funct_2, axiom,  (! [A, B] :  (? [C] : m1_funct_2(C, A, B)) ) ).
fof(existence_m1_pua2mss1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(C))  & m1_subset_1(C, k1_zfmisc_1(k4_partfun1(A, B)))) ) )  =>  (? [D] : m1_pua2mss1(D, A, B, C)) ) ) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(existence_m1_trees_3, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] : m1_trees_3(B, A)) ) ) ).
fof(existence_m2_aofa_i00, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_unialg_1(A) &  (v3_unialg_1(A) &  (v4_unialg_1(A) &  (v3_aofa_000(A) &  (v4_aofa_000(A) &  (v5_aofa_000(A) &  (v6_aofa_000(A) & l1_unialg_1(A)) ) ) ) ) ) ) )  &  ( ~ (v1_xboole_0(B))  &  (m1_subset_1(C, k1_zfmisc_1(k9_funct_2(B, k4_numbers))) & m1_aofa_000(D, A, k9_funct_2(B, k4_numbers), C)) ) )  =>  (? [E] : m2_aofa_i00(E, A, B, C, D)) ) ) ).
fof(existence_m2_finseq_1, axiom,  (! [A] :  (? [B] : m2_finseq_1(B, A)) ) ).
fof(existence_m2_funct_2, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(B))  & m1_funct_2(C, A, B))  =>  (? [D] : m2_funct_2(D, A, B, C)) ) ) ).
fof(existence_m4_aofa_i00, axiom,  (? [A] : m4_aofa_i00(A)) ).
fof(fc108_valued_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v4_relat_1(A, k4_ordinal1))  => v6_membered(k9_xtuple_0(A))) ) ).
fof(fc10_aofa_000, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_unialg_1(A) &  (v3_unialg_1(A) &  (v4_unialg_1(A) &  (v3_aofa_000(A) &  (v4_aofa_000(A) &  (v5_aofa_000(A) &  (v6_aofa_000(A) &  (v9_aofa_000(A) & l1_unialg_1(A)) ) ) ) ) ) ) ) )  =>  ~ (v1_finset_1(k18_aofa_000(A))) ) ) ).
fof(fc10_card_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  ( ~ (v1_finset_1(k1_card_1(A)))  & v1_card_1(k1_card_1(A))) ) ) ).
fof(fc10_card_3, axiom, v5_card_3(k4_ordinal1)).
fof(fc10_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(A)) )  => v1_setfam_1(k10_xtuple_0(A))) ) ).
fof(fc10_funct_2, axiom,  (! [A, B] : v4_funct_1(k1_funct_2(A, B))) ).
fof(fc10_membered, axiom,  (! [A] :  (v1_rat_1(A) => v4_membered(k1_tarski(A))) ) ).
fof(fc10_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) & v9_ordinal1(A))  =>  ~ (v10_ordinal1(k10_xtuple_0(A))) ) ) ).
fof(fc10_valued_0, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v4_valued_0(A))  &  (v1_relat_1(B) & v4_valued_0(B)) )  => v4_valued_0(k2_xboole_0(A, B))) ) ).
fof(fc11_aofa_000, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_unialg_1(A) &  (v3_unialg_1(A) &  (v4_unialg_1(A) &  (v3_aofa_000(A) &  (v4_aofa_000(A) &  (v5_aofa_000(A) &  (v6_aofa_000(A) & l1_unialg_1(A)) ) ) ) ) ) ) )  => v15_aofa_000(k12_aofa_000(A), A)) ) ).
fof(fc11_funct_1, axiom,  (! [A, B] :  ( ( ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(A)) ) )  & m1_subset_1(B, k9_xtuple_0(A)))  =>  ~ (v1_xboole_0(k1_funct_1(A, B))) ) ) ).
fof(fc11_membered, axiom,  (! [A] :  (v1_int_1(A) => v5_membered(k1_tarski(A))) ) ).
fof(fc11_nat_1, axiom,  (! [A] :  ( ~ (v8_ordinal1(A))  => v1_setfam_1(k1_tarski(A))) ) ).
fof(fc11_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) &  ~ (v9_ordinal1(A)) )  => v10_ordinal1(k10_xtuple_0(A))) ) ).
fof(fc11_valued_0, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v5_valued_0(A))  &  (v1_relat_1(B) & v5_valued_0(B)) )  => v5_valued_0(k2_xboole_0(A, B))) ) ).
fof(fc12_aofa_000, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_unialg_1(A) &  (v3_unialg_1(A) &  (v4_unialg_1(A) &  (v3_aofa_000(A) &  (v4_aofa_000(A) &  (v5_aofa_000(A) &  (v6_aofa_000(A) & l1_unialg_1(A)) ) ) ) ) ) ) )  &  ( (v15_aofa_000(B, A) & m1_subset_1(B, u1_struct_0(A)))  &  (v15_aofa_000(C, A) & m1_subset_1(C, u1_struct_0(A))) ) )  => v15_aofa_000(k13_aofa_000(A, B, C), A)) ) ).
fof(fc12_card_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  ~ (v1_finset_1(k1_zfmisc_1(A))) ) ) ).
fof(fc12_finset_1, axiom,  (! [A, B] :  (v1_finset_1(A) => v1_finset_1(k4_xboole_0(A, B))) ) ).
fof(fc12_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) )  => v1_zfmisc_1(k10_xtuple_0(A))) ) ).
fof(fc12_membered, axiom,  (! [A] :  (v7_ordinal1(A) => v6_membered(k1_tarski(A))) ) ).
fof(fc12_valued_0, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v6_valued_0(A))  &  (v1_relat_1(B) & v6_valued_0(B)) )  => v6_valued_0(k2_xboole_0(A, B))) ) ).
fof(fc13_card_1, axiom,  (! [A, B] :  ( ( ~ (v1_finset_1(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_finset_1(k2_zfmisc_1(A, B))) ) ) ).
fof(fc13_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) )  =>  ~ (v1_zfmisc_1(k10_xtuple_0(A))) ) ) ).
fof(fc14_card_1, axiom,  (! [A, B] :  ( ( ~ (v1_finset_1(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_finset_1(k2_zfmisc_1(B, A))) ) ) ).
fof(fc14_finset_1, axiom,  (! [A, B] :  ( (v1_finset_1(A) & v1_finset_1(B))  => v1_finset_1(k2_zfmisc_1(A, B))) ) ).
fof(fc14_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  => v4_funct_1(k1_tarski(A))) ) ).
fof(fc14_valued_0, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_valued_0(A))  & v1_relat_1(B))  => v1_valued_0(k4_xboole_0(A, B))) ) ).
fof(fc16_card_1, axiom,  (! [A] : v3_card_1(k1_tarski(A), 1)) ).
fof(fc16_valued_0, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v2_valued_0(A))  & v1_relat_1(B))  => v2_valued_0(k4_xboole_0(A, B))) ) ).
fof(fc17_card_1, axiom,  (! [A, B] :  ( (v1_card_1(A) &  (v1_relat_1(B) &  (v1_funct_1(B) & v3_card_1(B, A)) ) )  => v3_card_1(k9_xtuple_0(B), A)) ) ).
fof(fc17_finset_1, axiom,  (! [A] :  (v1_finset_1(A) => v1_finset_1(k1_zfmisc_1(A))) ) ).
fof(fc17_funct_1, axiom,  (! [A, B, C] :  ( (v4_funct_1(A) &  (v1_relat_1(C) &  (v5_relat_1(C, A) & v1_funct_1(C)) ) )  =>  (v1_relat_1(k1_funct_1(C, B)) & v1_funct_1(k1_funct_1(C, B))) ) ) ).
fof(fc18_abian, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v2_setfam_1(B))  &  ( (v2_relat_1(C) &  (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) )  & m1_subset_1(D, A)) ) )  =>  ~ (v1_xboole_0(k1_funct_1(C, D))) ) ) ).
fof(fc18_card_1, axiom,  (! [A, B] :  ( ( ~ (v1_zfmisc_1(A))  &  (v3_card_1(B, 1) & m1_subset_1(B, k1_zfmisc_1(A))) )  =>  ~ (v1_xboole_0(k4_xboole_0(A, B))) ) ) ).
fof(fc18_funct_1, axiom,  (! [A] :  ( ( ~ (v1_zfmisc_1(A))  &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  ~ (v1_zfmisc_1(k9_xtuple_0(A))) ) ) ).
fof(fc18_valued_0, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v3_valued_0(A))  & v1_relat_1(B))  => v3_valued_0(k4_xboole_0(A, B))) ) ).
fof(fc19_abian, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  ~ (v2_setfam_1(k1_zfmisc_1(A))) ) ) ).
fof(fc19_finset_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_finset_1(A))  => v1_finset_1(k9_xtuple_0(A))) ) ).
fof(fc19_struct_0, axiom,  (! [A, B] :  ( (v1_card_1(A) &  (v13_struct_0(B, A) & l1_struct_0(B)) )  => v3_card_1(u1_struct_0(B), A)) ) ).
fof(fc1_aofa_000, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  => v2_relat_1(k10_finseq_1(A, B))) ) ).
fof(fc1_aofa_i00, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_finset_1(B)) )  =>  ~ (v1_finset_1(k1_funct_2(A, B))) ) ) ).
fof(fc1_card_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (v1_xboole_0(k1_card_1(A)) & v1_card_1(k1_card_1(A))) ) ) ).
fof(fc1_finset_1, axiom,  (! [A] : v1_finset_1(k1_tarski(A))) ).
fof(fc1_freealg, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_finseq_1(A, k4_ordinal1))  =>  ( ~ (v2_struct_0(k3_freealg(A, B)))  & v1_lang1(k3_freealg(A, B))) ) ) ).
fof(fc1_funct_1, axiom,  (! [A, B] : v1_funct_1(k1_tarski(k4_tarski(A, B)))) ).
fof(fc1_funct_2, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  =>  ~ (v1_xboole_0(k1_funct_2(A, B))) ) ) ).
fof(fc1_membered, axiom, v1_membered(k2_numbers)).
fof(fc1_numbers, axiom,  ~ (v1_xboole_0(k1_numbers)) ).
fof(fc1_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v4_relat_1(B, A))  &  (v1_relat_1(C) & v4_relat_1(C, A)) )  => v4_relat_1(k2_xboole_0(B, C), A)) ) ).
fof(fc1_struct_0, axiom,  (! [A] :  ( (v2_struct_0(A) & l1_struct_0(A))  => v1_xboole_0(u1_struct_0(A))) ) ).
fof(fc1_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_valued_0(A))  => v1_membered(k10_xtuple_0(A))) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc1_xtuple_0, axiom,  (! [A, B] : v1_xtuple_0(k4_tarski(A, B))) ).
fof(fc20_valued_0, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v4_valued_0(A))  & v1_relat_1(B))  => v4_valued_0(k4_xboole_0(A, B))) ) ).
fof(fc22_finset_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_finset_1(A))  => v1_finset_1(k10_xtuple_0(A))) ) ).
fof(fc22_valued_0, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v5_valued_0(A))  & v1_relat_1(B))  => v5_valued_0(k4_xboole_0(A, B))) ) ).
fof(fc24_valued_0, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v6_valued_0(A))  & v1_relat_1(B))  => v6_valued_0(k4_xboole_0(A, B))) ) ).
fof(fc25_funcop_1, axiom,  (! [A, B, C] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  =>  (v1_relat_1(k1_binop_1(A, B, C)) & v1_funct_1(k1_binop_1(A, B, C))) ) ) ).
fof(fc25_membered, axiom,  (! [A, B] :  ( (v1_membered(A) & v1_membered(B))  => v1_membered(k2_xboole_0(A, B))) ) ).
fof(fc26_membered, axiom,  (! [A, B] :  ( (v2_membered(A) & v2_membered(B))  => v2_membered(k2_xboole_0(A, B))) ) ).
fof(fc27_membered, axiom,  (! [A, B] :  ( (v3_membered(A) & v3_membered(B))  => v3_membered(k2_xboole_0(A, B))) ) ).
fof(fc28_membered, axiom,  (! [A, B] :  ( (v4_membered(A) & v4_membered(B))  => v4_membered(k2_xboole_0(A, B))) ) ).
fof(fc29_membered, axiom,  (! [A, B] :  ( (v5_membered(A) & v5_membered(B))  => v5_membered(k2_xboole_0(A, B))) ) ).
fof(fc2_aofa_000, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v2_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) ) )  &  (v1_relat_1(B) &  (v2_relat_1(B) &  (v1_funct_1(B) & v1_finseq_1(B)) ) ) )  =>  (v1_relat_1(k7_finseq_1(A, B)) &  (v2_relat_1(k7_finseq_1(A, B)) &  (v1_funct_1(k7_finseq_1(A, B)) & v1_finseq_1(k7_finseq_1(A, B))) ) ) ) ) ).
fof(fc2_card_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (v8_ordinal1(k1_card_1(A)) & v1_card_1(k1_card_1(A))) ) ) ).
fof(fc2_freealg, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_finseq_1(A, k4_ordinal1))  =>  (v1_lang1(k3_freealg(A, B)) & v2_dtconstr(k3_freealg(A, B))) ) ) ).
fof(fc2_funct_2, axiom,  (! [A] :  ~ (v1_xboole_0(k1_funct_2(A, A))) ) ).
fof(fc2_membered, axiom, v2_membered(k6_numbers)).
fof(fc2_numbers, axiom,  ~ (v1_xboole_0(k2_numbers)) ).
fof(fc2_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_xboole_0(u1_struct_0(A))) ) ) ).
fof(fc2_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v2_valued_0(A))  => v2_membered(k10_xtuple_0(A))) ) ).
fof(fc2_xboole_0, axiom,  (! [A] :  ~ (v1_xboole_0(k1_tarski(A))) ) ).
fof(fc30_finset_1, axiom,  (! [A] :  (v1_finset_1(A) => v5_finset_1(k1_tarski(A))) ) ).
fof(fc30_membered, axiom,  (! [A, B] :  ( (v6_membered(A) & v6_membered(B))  => v6_membered(k2_xboole_0(A, B))) ) ).
fof(fc31_finset_1, axiom,  (! [A] :  (v1_finset_1(A) => v5_finset_1(k1_zfmisc_1(A))) ) ).
fof(fc33_finset_1, axiom,  (! [A, B] :  ( (v5_finset_1(A) & v5_finset_1(B))  => v5_finset_1(k2_xboole_0(A, B))) ) ).
fof(fc35_finset_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_finset_1(A)) )  => v1_finset_1(k1_funct_1(A, B))) ) ).
fof(fc36_finset_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v2_finset_1(A))  => v5_finset_1(k10_xtuple_0(A))) ) ).
fof(fc3_card_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  ( ~ (v1_xboole_0(k1_card_1(A)))  & v1_card_1(k1_card_1(A))) ) ) ).
fof(fc3_freealg, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v2_relat_1(A))  & m1_finseq_1(A, k4_ordinal1)) )  =>  (v1_lang1(k3_freealg(A, B)) &  (v2_dtconstr(k3_freealg(A, B)) & v3_dtconstr(k3_freealg(A, B))) ) ) ) ).
fof(fc3_funct_2, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & v1_xboole_0(B))  => v1_xboole_0(k1_funct_2(A, B))) ) ).
fof(fc3_membered, axiom, v3_membered(k1_numbers)).
fof(fc3_numbers, axiom,  ~ (v1_xboole_0(k3_numbers)) ).
fof(fc3_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v4_relat_1(B, A))  & v1_relat_1(C))  => v4_relat_1(k4_xboole_0(B, C), A)) ) ).
fof(fc3_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v3_valued_0(A))  => v3_membered(k10_xtuple_0(A))) ) ).
fof(fc43_membered, axiom,  (! [A, B] :  (v1_membered(A) => v1_membered(k4_xboole_0(A, B))) ) ).
fof(fc44_membered, axiom,  (! [A, B] :  (v2_membered(A) => v2_membered(k4_xboole_0(A, B))) ) ).
fof(fc45_membered, axiom,  (! [A, B] :  (v3_membered(A) => v3_membered(k4_xboole_0(A, B))) ) ).
fof(fc46_membered, axiom,  (! [A, B] :  (v4_membered(A) => v4_membered(k4_xboole_0(A, B))) ) ).
fof(fc47_membered, axiom,  (! [A, B] :  (v5_membered(A) => v5_membered(k4_xboole_0(A, B))) ) ).
fof(fc48_membered, axiom,  (! [A, B] :  (v6_membered(A) => v6_membered(k4_xboole_0(A, B))) ) ).
fof(fc4_card_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  ( ~ (v8_ordinal1(k1_card_1(A)))  & v1_card_1(k1_card_1(A))) ) ) ).
fof(fc4_freealg, axiom,  (! [A, B] :  ( ( ( ~ (v1_xboole_0(A))  & m1_finseq_1(A, k4_ordinal1))  &  ( ~ (v1_xboole_0(B))  & v1_freealg(B)) )  =>  (v1_lang1(k3_freealg(A, B)) &  (v1_dtconstr(k3_freealg(A, B)) &  (v2_dtconstr(k3_freealg(A, B)) & v3_dtconstr(k3_freealg(A, B))) ) ) ) ) ).
fof(fc4_membered, axiom, v4_membered(k3_numbers)).
fof(fc4_numbers, axiom,  ~ (v1_xboole_0(k4_numbers)) ).
fof(fc4_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v5_ordinal1(A)) )  => v3_ordinal1(k9_xtuple_0(A))) ) ).
fof(fc4_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v5_relat_1(B, A))  &  (v1_relat_1(C) & v5_relat_1(C, A)) )  => v5_relat_1(k2_xboole_0(B, C), A)) ) ).
fof(fc4_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v4_valued_0(A))  => v4_membered(k10_xtuple_0(A))) ) ).
fof(fc4_xboole_0, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_xboole_0(A, B))) ) ) ).
fof(fc4_xtuple_0, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k9_xtuple_0(A))) ) ).
fof(fc55_membered, axiom, v7_membered(k2_numbers)).
fof(fc56_membered, axiom, v7_membered(k1_numbers)).
fof(fc57_membered, axiom, v7_membered(k3_numbers)).
fof(fc58_membered, axiom, v7_membered(k4_numbers)).
fof(fc59_membered, axiom, v7_membered(k4_ordinal1)).
fof(fc5_freealg, axiom,  (! [A, B] :  ( ( ( ~ (v1_xboole_0(A))  & m1_finseq_1(A, k4_ordinal1))  &  ( ~ (v1_xboole_0(B))  & v1_freealg(B)) )  =>  ( ~ (v2_struct_0(k7_freealg(A, B)))  &  (v1_unialg_1(k7_freealg(A, B)) &  (v2_unialg_1(k7_freealg(A, B)) &  (v3_unialg_1(k7_freealg(A, B)) &  (v4_unialg_1(k7_freealg(A, B)) & v3_freealg(k7_freealg(A, B))) ) ) ) ) ) ) ).
fof(fc5_membered, axiom, v5_membered(k4_numbers)).
fof(fc5_numbers, axiom,  ~ (v1_xboole_0(k6_numbers)) ).
fof(fc5_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_valued_0(A))  => v5_membered(k10_xtuple_0(A))) ) ).
fof(fc5_xboole_0, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_xboole_0(B, A))) ) ) ).
fof(fc5_xtuple_0, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k10_xtuple_0(A))) ) ).
fof(fc61_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_valued_0(A)) )  => v1_xcmplx_0(k1_funct_1(A, B))) ) ).
fof(fc62_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_valued_0(A)) )  => v1_xxreal_0(k1_funct_1(A, B))) ) ).
fof(fc63_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v3_valued_0(A)) )  => v1_xreal_0(k1_funct_1(A, B))) ) ).
fof(fc64_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v4_valued_0(A)) )  => v1_rat_1(k1_funct_1(A, B))) ) ).
fof(fc65_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v5_valued_0(A)) )  => v1_int_1(k1_funct_1(A, B))) ) ).
fof(fc66_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v6_valued_0(A)) )  => v7_ordinal1(k1_funct_1(A, B))) ) ).
fof(fc6_aofa_000, axiom,  (! [A, B] : v1_freealg(k2_zfmisc_1(A, B))) ).
fof(fc6_card_1, axiom, v1_card_1(k4_ordinal1)).
fof(fc6_membered, axiom, v6_membered(k4_ordinal1)).
fof(fc6_numbers, axiom,  ~ (v1_finset_1(k4_numbers)) ).
fof(fc6_ordinal1, axiom,  ( ~ (v1_xboole_0(k4_ordinal1))  & v3_ordinal1(k4_ordinal1)) ).
fof(fc6_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v5_relat_1(B, A))  & v1_relat_1(C))  => v5_relat_1(k4_xboole_0(B, C), A)) ) ).
fof(fc6_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(fc6_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v6_valued_0(A))  => v6_membered(k10_xtuple_0(A))) ) ).
fof(fc7_aofa_000, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_freealg(A))  =>  ( ~ (v2_struct_0(k7_freealg(k19_aofa_000, A)))  &  (v1_unialg_1(k7_freealg(k19_aofa_000, A)) &  (v2_unialg_1(k7_freealg(k19_aofa_000, A)) &  (v3_unialg_1(k7_freealg(k19_aofa_000, A)) &  (v4_unialg_1(k7_freealg(k19_aofa_000, A)) &  (v3_aofa_000(k7_freealg(k19_aofa_000, A)) &  (v4_aofa_000(k7_freealg(k19_aofa_000, A)) &  (v5_aofa_000(k7_freealg(k19_aofa_000, A)) & v6_aofa_000(k7_freealg(k19_aofa_000, A))) ) ) ) ) ) ) ) ) ) ).
fof(fc7_card_1, axiom, v2_card_1(k4_ordinal1)).
fof(fc7_card_3, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  => v2_card_3(k1_tarski(A))) ) ).
fof(fc7_membered, axiom,  (! [A] :  (v1_xcmplx_0(A) => v1_membered(k1_tarski(A))) ) ).
fof(fc7_numbers, axiom,  ~ (v1_finset_1(k3_numbers)) ).
fof(fc7_struct_0, axiom,  (! [A] :  ( (v7_struct_0(A) & l1_struct_0(A))  => v1_zfmisc_1(u1_struct_0(A))) ) ).
fof(fc7_valued_0, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_valued_0(A))  &  (v1_relat_1(B) & v1_valued_0(B)) )  => v1_valued_0(k2_xboole_0(A, B))) ) ).
fof(fc85_valued_0, axiom,  (! [A, B] :  (v1_membered(B) => v1_valued_0(k2_zfmisc_1(A, B))) ) ).
fof(fc86_valued_0, axiom,  (! [A, B] :  (v2_membered(B) => v2_valued_0(k2_zfmisc_1(A, B))) ) ).
fof(fc87_valued_0, axiom,  (! [A, B] :  (v3_membered(B) => v3_valued_0(k2_zfmisc_1(A, B))) ) ).
fof(fc88_valued_0, axiom,  (! [A, B] :  (v4_membered(B) => v4_valued_0(k2_zfmisc_1(A, B))) ) ).
fof(fc89_valued_0, axiom,  (! [A, B] :  (v5_membered(B) => v5_valued_0(k2_zfmisc_1(A, B))) ) ).
fof(fc8_aofa_000, axiom,  (! [A] :  ( ( ~ (v1_finset_1(A))  & v1_freealg(A))  =>  ( ~ (v2_struct_0(k7_freealg(k19_aofa_000, A)))  &  (v1_unialg_1(k7_freealg(k19_aofa_000, A)) &  (v2_unialg_1(k7_freealg(k19_aofa_000, A)) &  (v3_unialg_1(k7_freealg(k19_aofa_000, A)) &  (v4_unialg_1(k7_freealg(k19_aofa_000, A)) & v9_aofa_000(k7_freealg(k19_aofa_000, A))) ) ) ) ) ) ) ).
fof(fc8_card_1, axiom,  (! [A] :  (v1_finset_1(A) =>  (v1_finset_1(k1_card_1(A)) & v1_card_1(k1_card_1(A))) ) ) ).
fof(fc8_membered, axiom,  (! [A] :  (v1_xxreal_0(A) => v2_membered(k1_tarski(A))) ) ).
fof(fc8_numbers, axiom,  ~ (v1_finset_1(k1_numbers)) ).
fof(fc8_ordinal1, axiom, v7_ordinal1(k5_ordinal1)).
fof(fc8_relset_1, axiom,  (! [A, B, C, D] :  (m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, B), C))) => v1_relat_1(k9_xtuple_0(D))) ) ).
fof(fc8_struct_0, axiom,  (! [A] :  ( (v8_struct_0(A) & l1_struct_0(A))  => v1_finset_1(u1_struct_0(A))) ) ).
fof(fc8_valued_0, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v2_valued_0(A))  &  (v1_relat_1(B) & v2_valued_0(B)) )  => v2_valued_0(k2_xboole_0(A, B))) ) ).
fof(fc90_valued_0, axiom,  (! [A, B] :  (v6_membered(B) => v6_valued_0(k2_zfmisc_1(A, B))) ) ).
fof(fc9_aofa_000, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_freealg(A))  =>  ( ~ (v2_struct_0(k7_freealg(k19_aofa_000, A)))  &  (v1_unialg_1(k7_freealg(k19_aofa_000, A)) &  (v2_unialg_1(k7_freealg(k19_aofa_000, A)) &  (v3_unialg_1(k7_freealg(k19_aofa_000, A)) &  (v4_unialg_1(k7_freealg(k19_aofa_000, A)) & v12_aofa_000(k7_freealg(k19_aofa_000, A))) ) ) ) ) ) ) ).
fof(fc9_card_1, axiom,  ~ (v1_finset_1(k4_ordinal1)) ).
fof(fc9_finset_1, axiom,  (! [A, B] :  ( (v1_finset_1(A) & v1_finset_1(B))  => v1_finset_1(k2_xboole_0(A, B))) ) ).
fof(fc9_funcop_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  =>  (v1_relat_1(k1_funct_1(A, B)) & v1_funct_1(k1_funct_1(A, B))) ) ) ).
fof(fc9_membered, axiom,  (! [A] :  (v1_xreal_0(A) => v3_membered(k1_tarski(A))) ) ).
fof(fc9_numbers, axiom,  ~ (v1_finset_1(k2_numbers)) ).
fof(fc9_ordinal1, axiom, v8_ordinal1(k5_ordinal1)).
fof(fc9_relset_1, axiom,  (! [A, B, C, D] :  (m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, k2_zfmisc_1(B, C)))) => v1_relat_1(k10_xtuple_0(D))) ) ).
fof(fc9_struct_0, axiom,  (! [A] :  ( ( ~ (v8_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_finset_1(u1_struct_0(A))) ) ) ).
fof(fc9_valued_0, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v3_valued_0(A))  &  (v1_relat_1(B) & v3_valued_0(B)) )  => v3_valued_0(k2_xboole_0(A, B))) ) ).
fof(fraenkel_a_1_1_aofa_000, axiom,  (! [A, B] :  ( ( ~ (v2_struct_0(B))  &  (v2_unialg_1(B) &  (v3_unialg_1(B) &  (v4_unialg_1(B) &  (v3_aofa_000(B) &  (v4_aofa_000(B) &  (v5_aofa_000(B) &  (v6_aofa_000(B) & l1_unialg_1(B)) ) ) ) ) ) ) )  =>  (r2_hidden(A, a_1_1_aofa_000(B)) <=>  (? [C, D] :  ( (m1_subset_1(C, u1_struct_0(B)) & m1_subset_1(D, u1_struct_0(B)))  &  (A=k13_aofa_000(B, C, D) &  ( ~ (C=k13_aofa_000(B, C, D))  &  ~ (D=k13_aofa_000(B, C, D)) ) ) ) ) ) ) ) ).
fof(fraenkel_a_2_0_freealg, axiom,  (! [A, B, C] :  ( ( ( ~ (v1_xboole_0(B))  & m2_finseq_1(B, k4_ordinal1))  &  ( ~ (v1_xboole_0(C))  & v1_freealg(C)) )  =>  (r2_hidden(A, a_2_0_freealg(B, C)) <=>  (? [D] :  (m1_subset_1(D, u1_struct_0(k3_freealg(B, C))) &  (A=k2_trees_4(u1_struct_0(k3_freealg(B, C)), D) & r2_tarski(D, k6_dtconstr(k3_freealg(B, C)))) ) ) ) ) ) ).
fof(fraenkel_a_3_0_aofa_i00, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(B))  & v4_funct_1(B))  =>  (r2_hidden(A, a_3_0_aofa_i00(B, C, D)) <=>  (? [E] :  (m1_subset_1(E, B) &  (A=E &  ~ (k1_funct_1(E, C)=D) ) ) ) ) ) ) ).
fof(free_g1_lang1, axiom,  (! [A, B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k3_finseq_2(A)))) =>  (! [C, D] :  (g1_lang1(A, B)=g1_lang1(C, D) =>  (A=C & B=D) ) ) ) ) ).
fof(free_g1_unialg_1, axiom,  (! [A, B] :  (m1_finseq_1(B, k4_partfun1(k3_finseq_2(A), A)) =>  (! [C, D] :  (g1_unialg_1(A, B)=g1_unialg_1(C, D) =>  (A=C & B=D) ) ) ) ) ).
fof(idempotence_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, A)=A) ).
fof(projectivity_k1_card_1, axiom,  (! [A] : k1_card_1(k1_card_1(A))=k1_card_1(A)) ).
fof(rc10_card_1, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_card_1(B)) ) ) ) ).
fof(rc10_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v1_funct_1(A) & v2_finset_1(A)) ) ) ) ).
fof(rc10_ordinal1, axiom,  (? [A] :  ~ (v8_ordinal1(A)) ) ).
fof(rc11_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) ) ) ).
fof(rc12_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) & v9_ordinal1(A)) ) ).
fof(rc13_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) &  ~ (v9_ordinal1(A)) ) ) ).
fof(rc1_card_1, axiom,  (? [A] : v1_card_1(A)) ).
fof(rc1_card_3, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v1_card_3(A)) ) ) ).
fof(rc1_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_finset_1(A)) ) ).
fof(rc1_freealg, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_freealg(A)) ) ).
fof(rc1_funcop_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) ) ) ).
fof(rc1_funct_1, axiom,  (? [A] :  (v1_relat_1(A) & v1_funct_1(A)) ) ).
fof(rc1_funct_2, axiom,  (! [A, B] :  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) & v1_funct_2(C, A, B)) ) ) ) ) ) ) ).
fof(rc1_int_1, axiom,  (? [A] :  (v1_xxreal_0(A) &  (v1_xcmplx_0(A) &  (v1_xreal_0(A) & v1_int_1(A)) ) ) ) ).
fof(rc1_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v6_membered(A)) ) ).
fof(rc1_nat_1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc1_ordinal1, axiom,  (? [A] :  (v1_ordinal1(A) & v2_ordinal1(A)) ) ).
fof(rc1_relset_1, axiom,  (! [A, B] :  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_xboole_0(C) &  (v1_relat_1(C) &  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ) ) ).
fof(rc1_valued_0, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v6_valued_0(A)) ) ) ).
fof(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc1_xcmplx_0, axiom,  (? [A] : v1_xcmplx_0(A)) ).
fof(rc1_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc1_xtuple_0, axiom,  (? [A] : v1_xtuple_0(A)) ).
fof(rc1_xxreal_0, axiom,  (? [A] : v1_xxreal_0(A)) ).
fof(rc21_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ( ~ (v1_xboole_0(B))  & v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc22_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ~ (v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc23_struct_0, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] :  (l1_struct_0(B) & v13_struct_0(B, A)) ) ) ) ).
fof(rc2_card_1, axiom,  (? [A] :  (v1_ordinal1(A) &  (v2_ordinal1(A) &  (v3_ordinal1(A) &  (v1_finset_1(A) & v1_card_1(A)) ) ) ) ) ).
fof(rc2_finset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_finset_1(B)) ) ) ).
fof(rc2_funcop_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  (v3_funct_1(A) &  ~ (v1_xboole_0(A)) ) ) ) ) ).
fof(rc2_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) ) ) ).
fof(rc2_int_1, axiom,  (? [A] : v1_int_1(A)) ).
fof(rc2_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v6_membered(A)) ) ).
fof(rc2_nat_1, axiom,  (? [A] :  (v7_ordinal1(A) & v8_ordinal1(A)) ) ).
fof(rc2_ordinal1, axiom,  (? [A] : v3_ordinal1(A)) ).
fof(rc2_valued_0, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  (v3_funct_1(A) &  ( ~ (v1_xboole_0(A))  &  (v4_valued_0(A) &  (v5_valued_0(A) & v6_valued_0(A)) ) ) ) ) ) ) ).
fof(rc2_valued_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  ~ (v1_xboole_0(A)) ) ) ) ) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(rc2_xcmplx_0, axiom,  (? [A] : v1_xcmplx_0(A)) ).
fof(rc2_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc2_xxreal_0, axiom,  (? [A] : v1_xxreal_0(A)) ).
fof(rc3_card_1, axiom,  (? [A] :  ~ (v1_finset_1(A)) ) ).
fof(rc3_card_3, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v4_funct_1(A) & v2_card_3(A)) ) ) ).
fof(rc3_finset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ( ~ (v1_xboole_0(B))  & v1_finset_1(B)) ) ) ) ) ).
fof(rc3_funcop_1, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  =>  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) &  (v3_funct_1(C) &  (v1_partfun1(C, A) & v1_funct_2(C, A, B)) ) ) ) ) ) ) ) ) ) ).
fof(rc3_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(A)) ) ) ).
fof(rc3_int_1, axiom,  (? [A] : v2_int_1(A)) ).
fof(rc3_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v6_membered(A) & v7_membered(A)) ) ) ).
fof(rc3_nat_1, axiom,  (? [A] :  (v7_ordinal1(A) &  ~ (v8_ordinal1(A)) ) ) ).
fof(rc3_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_ordinal1(A) &  (v2_ordinal1(A) & v3_ordinal1(A)) ) ) ) ).
fof(rc3_valued_0, axiom,  (? [A] :  (m1_subset_1(A, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k4_ordinal1))) &  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v5_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  ( ~ (v1_xboole_0(A))  &  (v1_partfun1(A, k4_ordinal1) &  (v1_funct_2(A, k4_ordinal1, k4_ordinal1) &  (v1_valued_0(A) &  (v2_valued_0(A) &  (v3_valued_0(A) &  (v4_valued_0(A) &  (v5_valued_0(A) &  (v6_valued_0(A) & v7_valued_0(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc3_valued_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  ( ~ (v1_xboole_0(A))  & v1_finset_1(A)) ) ) ) ) ).
fof(rc3_xcmplx_0, axiom,  (? [A] :  (v8_ordinal1(A) & v1_xcmplx_0(A)) ) ).
fof(rc3_xreal_0, axiom,  (? [A] :  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v2_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc3_xxreal_0, axiom,  (? [A] :  (v1_xxreal_0(A) & v2_xxreal_0(A)) ) ).
fof(rc4_card_1, axiom,  (? [A] :  (v7_ordinal1(A) &  ~ (v8_ordinal1(A)) ) ) ).
fof(rc4_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v1_funct_1(A) & v1_finset_1(A)) ) ) ) ).
fof(rc4_freealg, axiom,  (? [A] :  (l1_unialg_1(A) &  ( ~ (v2_struct_0(A))  &  (v1_unialg_1(A) &  (v2_unialg_1(A) &  (v3_unialg_1(A) &  (v4_unialg_1(A) & v3_freealg(A)) ) ) ) ) ) ) ).
fof(rc4_funcop_1, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  =>  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) ) ) ) ) ) ) ).
fof(rc4_funct_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(A)) ) ) ) ).
fof(rc4_nat_1, axiom,  (? [A] :  (m1_subset_1(A, k1_zfmisc_1(k1_numbers)) &  ( ~ (v1_xboole_0(A))  & v3_ordinal1(A)) ) ) ).
fof(rc4_ordinal1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v1_funct_1(B) & v5_ordinal1(B)) ) ) ) ) ).
fof(rc4_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(rc4_valued_0, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, A))) &  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  (v3_funct_1(B) & v1_funct_2(B, k4_ordinal1, A)) ) ) ) ) ) ) ) ).
fof(rc4_valued_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  (v1_finset_1(A) & v3_card_1(A, 1)) ) ) ) ) ).
fof(rc4_xcmplx_0, axiom,  (? [A] :  ( ~ (v8_ordinal1(A))  & v1_xcmplx_0(A)) ) ).
fof(rc4_xreal_0, axiom,  (? [A] :  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v3_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc4_xxreal_0, axiom,  (? [A] :  (v1_xxreal_0(A) & v3_xxreal_0(A)) ) ).
fof(rc5_aofa_000, axiom,  (? [A] :  ( ~ (v1_finset_1(A))  & v1_freealg(A)) ) ).
fof(rc5_card_1, axiom,  (? [A] :  (v1_ordinal1(A) &  (v2_ordinal1(A) &  (v3_ordinal1(A) &  (v7_ordinal1(A) &  ( ~ (v8_ordinal1(A))  & v1_card_1(A)) ) ) ) ) ) ).
fof(rc5_card_3, axiom,  (? [A] : v5_card_3(A)) ).
fof(rc5_freealg, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_unialg_1(A) &  (v3_unialg_1(A) &  (v4_unialg_1(A) &  (v3_freealg(A) & l1_unialg_1(A)) ) ) ) )  =>  (? [B] :  (m1_freealg(B, A) & v2_freealg(B, A)) ) ) ) ).
fof(rc5_funcop_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) ) ) ) ).
fof(rc5_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) ) ) ).
fof(rc5_nat_1, axiom,  (? [A] :  (m1_subset_1(A, k4_ordinal1) &  (v1_ordinal1(A) &  (v2_ordinal1(A) &  (v3_ordinal1(A) &  (v7_ordinal1(A) &  ( ~ (v8_ordinal1(A))  &  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v1_xreal_0(A) &  (v1_finset_1(A) & v1_card_1(A)) ) ) ) ) ) ) ) ) ) ) ).
fof(rc5_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc5_valued_0, axiom,  (! [A] :  ( ~ (v2_setfam_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, A))) &  (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  ( ~ (v1_xboole_0(B))  &  (v1_partfun1(B, k4_ordinal1) & v1_funct_2(B, k4_ordinal1, A)) ) ) ) ) ) ) ) ) ) ) ).
fof(rc5_valued_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v5_relat_1(B, k4_ordinal1) &  (v1_funct_1(B) &  (v1_partfun1(B, A) &  (v1_valued_0(B) &  (v2_valued_0(B) &  (v3_valued_0(B) &  (v4_valued_0(B) &  (v5_valued_0(B) & v6_valued_0(B)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc5_xcmplx_0, axiom,  (? [A] :  ( ~ (v8_ordinal1(A))  & v1_xcmplx_0(A)) ) ).
fof(rc5_xreal_0, axiom,  (? [A] :  (v8_ordinal1(A) &  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc5_xxreal_0, axiom,  (? [A] :  (v8_ordinal1(A) & v1_xxreal_0(A)) ) ).
fof(rc6_aofa_000, axiom,  (? [A] :  (l1_unialg_1(A) &  ( ~ (v2_struct_0(A))  &  (v1_unialg_1(A) &  (v2_unialg_1(A) &  (v3_unialg_1(A) &  (v4_unialg_1(A) &  (v3_freealg(A) &  (v3_aofa_000(A) &  (v4_aofa_000(A) &  (v5_aofa_000(A) &  (v6_aofa_000(A) &  (v9_aofa_000(A) &  ( ~ (v10_aofa_000(A))  &  (v11_aofa_000(A) & v12_aofa_000(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc6_card_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_finset_1(B)) ) ) ) ) ).
fof(rc6_card_3, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v1_finset_1(A)) ) ) ) ).
fof(rc6_finset_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) & v1_finset_1(C)) ) ) ) ) ) ).
fof(rc6_funct_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) & v1_funct_1(C)) ) ) ) ) ).
fof(rc6_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc6_valued_0, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) & v6_valued_0(B)) ) ) ) ) ) ).
fof(rc7_aofa_000, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_unialg_1(A) &  (v3_unialg_1(A) &  (v4_unialg_1(A) &  (v3_aofa_000(A) &  (v4_aofa_000(A) &  (v5_aofa_000(A) &  (v6_aofa_000(A) & l1_unialg_1(A)) ) ) ) ) ) ) )  =>  (? [B] :  (m1_subset_1(B, u1_struct_0(A)) & v15_aofa_000(B, A)) ) ) ) ).
fof(rc7_card_1, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] : v3_card_1(B, A)) ) ) ).
fof(rc7_finset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  (? [C] :  ( ~ (v1_xboole_0(C))  &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) & v1_finset_1(C)) ) ) ) ) ) ) ) ).
fof(rc7_funct_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v4_funct_1(A)) ) ).
fof(rc7_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v7_ordinal1(A)) ) ).
fof(rc8_abian, axiom,  (! [A, B] :  ( ~ (v2_setfam_1(B))  =>  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_relat_1(C) &  (v2_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) & v1_funct_2(C, A, B)) ) ) ) ) ) ) ) ) ).
fof(rc8_card_1, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] :  (v1_relat_1(B) &  (v1_funct_1(B) & v3_card_1(B, A)) ) ) ) ) ).
fof(rc8_finset_1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ( ~ (v1_zfmisc_1(B))  & v1_finset_1(B)) ) ) ) ) ).
fof(rc8_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rc9_card_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v3_card_1(B, 1)) ) ) ) ).
fof(rc9_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_finset_1(A) & v5_finset_1(A)) ) ) ).
fof(rc9_funct_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, A) & v1_funct_1(B)) ) ) ) ) ).
fof(rc9_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rd1_card_1, axiom,  (! [A] :  (v1_card_1(A) => k1_card_1(A)=A) ) ).
fof(rd1_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) => k10_subset_1(A, k4_ordinal1)=A) ) ).
fof(rd1_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) => k10_subset_1(A, k2_numbers)=A) ) ).
fof(rd1_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => k10_subset_1(A, k1_numbers)=A) ) ).
fof(rd1_xxreal_0, axiom,  (! [A] :  (v1_xxreal_0(A) => k10_subset_1(A, k6_numbers)=A) ) ).
fof(rd2_xcmplx_0, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k10_subset_1(k4_tarski(A, B), k2_zfmisc_1(k2_numbers, k2_numbers))=k4_tarski(A, B)) ) ).
fof(rd2_xxreal_0, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  => k10_subset_1(k4_tarski(A, B), k2_zfmisc_1(k6_numbers, k6_numbers))=k4_tarski(A, B)) ) ).
fof(rd5_int_1, axiom,  (! [A] :  (v1_int_1(A) => k10_subset_1(A, k4_numbers)=A) ) ).
fof(rd6_int_1, axiom,  (! [A, B] :  ( (v1_int_1(A) & v1_int_1(B))  => k10_subset_1(k4_tarski(A, B), k2_zfmisc_1(k4_numbers, k4_numbers))=k4_tarski(A, B)) ) ).
fof(redefinition_k12_freealg, axiom,  (! [A, B] :  ( ( ( ~ (v1_xboole_0(A))  & m1_finseq_1(A, k4_ordinal1))  &  ( ~ (v1_xboole_0(B))  & v1_freealg(B)) )  => k12_freealg(A, B)=k8_freealg(A, B)) ) ).
fof(redefinition_k14_funct_7, axiom,  (! [A, B, C, D, E] :  ( ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  & m1_subset_1(E, B))  => k14_funct_7(A, B, C, D, E)=k1_funct_7(C, D, E)) ) ).
fof(redefinition_k1_pua2mss1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_finseq_1(B, k4_partfun1(k3_finseq_2(A), A)))  => k1_pua2mss1(A, B)=k10_xtuple_0(B)) ) ).
fof(redefinition_k21_aofa_i00, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  (m1_subset_1(C, k9_funct_2(A, B)) & m1_subset_1(D, A)) ) )  => k21_aofa_i00(A, B, C, D)=k1_funct_1(C, D)) ) ).
fof(redefinition_k2_binop_1, axiom,  (! [A, B, C, D, E, F] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( (v1_funct_1(D) &  (v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, B), C)))) )  &  (m1_subset_1(E, A) & m1_subset_1(F, B)) ) ) )  => k2_binop_1(A, B, C, D, E, F)=k1_binop_1(D, E, F)) ) ).
fof(redefinition_k2_finseq_4, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  (m1_subset_1(B, A) & m1_subset_1(C, A)) )  => k2_finseq_4(A, B, C)=k10_finseq_1(B, C)) ) ).
fof(redefinition_k2_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  => k2_relset_1(A, B)=k10_xtuple_0(B)) ) ).
fof(redefinition_k2_trees_4, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(B, A))  => k2_trees_4(A, B)=k1_trees_4(B)) ) ).
fof(redefinition_k3_finseq_2, axiom,  (! [A] : k3_finseq_2(A)=k13_finseq_1(A)) ).
fof(redefinition_k3_funct_2, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  & m1_subset_1(D, A)) )  => k3_funct_2(A, B, C, D)=k1_funct_1(C, D)) ) ).
fof(redefinition_k4_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  => k4_finseq_1(A)=k9_xtuple_0(A)) ) ).
fof(redefinition_k5_numbers, axiom, k5_numbers=k5_ordinal1).
fof(redefinition_k6_dtconstr, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v1_dtconstr(A) & l1_lang1(A)) )  => k6_dtconstr(A)=k1_lang1(A)) ) ).
fof(redefinition_k6_subset_1, axiom,  (! [A, B] : k6_subset_1(A, B)=k4_xboole_0(A, B)) ).
fof(redefinition_k7_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(B, k1_zfmisc_1(A)) => k7_subset_1(A, B, C)=k4_xboole_0(B, C)) ) ).
fof(redefinition_k8_finseq_1, axiom,  (! [A, B, C] :  ( (m1_finseq_1(B, A) & m1_finseq_1(C, A))  => k8_finseq_1(A, B, C)=k7_finseq_1(B, C)) ) ).
fof(redefinition_k9_funct_2, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  => k9_funct_2(A, B)=k1_funct_2(A, B)) ) ).
fof(redefinition_m1_pua2mss1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(C))  & m1_subset_1(C, k1_zfmisc_1(k4_partfun1(A, B)))) ) )  =>  (! [D] :  (m1_pua2mss1(D, A, B, C) <=> m1_subset_1(D, C)) ) ) ) ).
fof(redefinition_m2_finseq_1, axiom,  (! [A] :  (! [B] :  (m2_finseq_1(B, A) <=> m1_finseq_1(B, A)) ) ) ).
fof(redefinition_m2_funct_2, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(B))  & m1_funct_2(C, A, B))  =>  (! [D] :  (m2_funct_2(D, A, B, C) <=> m1_subset_1(D, C)) ) ) ) ).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(spc1_numerals, axiom,  (v2_xxreal_0(1) & m1_subset_1(1, k4_ordinal1)) ).
fof(spc2_boole, axiom,  ~ (v1_xboole_0(2)) ).
fof(spc2_numerals, axiom,  (v2_xxreal_0(2) & m1_subset_1(2, k4_ordinal1)) ).
fof(spc3_boole, axiom,  ~ (v1_xboole_0(3)) ).
fof(spc3_numerals, axiom,  (v2_xxreal_0(3) & m1_subset_1(3, k4_ordinal1)) ).
fof(spc4_boole, axiom,  ~ (v1_xboole_0(4)) ).
fof(spc4_numerals, axiom,  (v2_xxreal_0(4) & m1_subset_1(4, k4_ordinal1)) ).
fof(t16_aofa_i00, axiom,  (! [A] :  (m4_aofa_i00(A) =>  (! [B] :  ( (v1_funct_1(B) &  (v1_funct_2(B, k9_funct_2(k4_ordinal1, k4_numbers), k4_ordinal1) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k9_funct_2(k4_ordinal1, k4_numbers), k4_ordinal1)))) )  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, k9_funct_2(k4_ordinal1, k4_numbers), k4_numbers) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k9_funct_2(k4_ordinal1, k4_numbers), k4_numbers)))) )  => r2_aofa_i00(k7_freealg(k19_aofa_000, k26_aofa_i00), k4_ordinal1, k1_aofa_i00(k9_funct_2(k4_ordinal1, k4_numbers), k5_numbers, k5_numbers), A, B, C)) ) ) ) ) ) ).
fof(t1_boole, axiom,  (! [A] : k2_xboole_0(A, k1_xboole_0)=A) ).
fof(t1_numerals, axiom, m1_subset_1(k1_xboole_0, k4_ordinal1)).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t2_tarski, axiom,  (! [A] :  (! [B] :  ( (! [C] :  (r2_hidden(C, A) <=> r2_hidden(C, B)) )  => A=B) ) ) ).
fof(t3_boole, axiom,  (! [A] : k4_xboole_0(A, k1_xboole_0)=A) ).
fof(t3_freealg, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & m2_finseq_1(A, k4_ordinal1))  =>  (! [B] :  (v1_freealg(B) => k1_lang1(k3_freealg(A, B))=B) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t4_boole, axiom,  (! [A] : k4_xboole_0(k1_xboole_0, A)=k1_xboole_0) ).
fof(t4_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r2_tarski(A, B) & m1_subset_1(B, k1_zfmisc_1(C)))  => m1_subset_1(A, C)) ) ) ) ).
fof(t5_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ~ ( (r2_tarski(A, B) &  (m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)) ) ) ) ) ) ).
fof(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
fof(t70_aofa_000, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_freealg(A))  =>  (k18_aofa_000(k7_freealg(k19_aofa_000, A))=k12_freealg(k19_aofa_000, A) & k1_card_1(A)=k1_card_1(k12_freealg(k19_aofa_000, A))) ) ) ).
fof(t7_boole, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(A, B) & v1_xboole_0(B)) ) ) ) ).
fof(t87_zfmisc_1, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] :  (r2_hidden(k4_tarski(C, D), k2_zfmisc_1(A, B)) <=>  (r2_hidden(C, A) & r2_hidden(D, B)) ) ) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
fof(t8_funct_2, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  =>  ( (B=k1_xboole_0 => A=k1_xboole_0)  => r2_tarski(C, k1_funct_2(A, B))) ) ) ) ) ).
